摘要
为同时高精度逼近速度和位移,利用时间间断的时空有限元与降阶的思想,对一类电报方程的初边值问题建立一种时间间断时空有限元格式.利用有限差分方法与有限元方法相结合的技巧,证明了格式的稳定性和收敛性,得到了速度的L~∞(L^2)模和位移的L~∞(H^1)模最优误差估计.最后用数值算例验证了理论分析结果和所提算法的有效性.
To approximate displacement and velocity with high accuracy at the same time, a time discontinuous space-time finite element method for a kind of initial boundary value problems of telegraph equations is constructed by using the time discontinuous space-time finite element and the order-reduced idea. The stability and convergence for the proposed scheme are proved by using the technique of combining finite difference method and finite element method. The optimal order L∞ （L2） norm error estimate for velocity and L∞ （H1） norm error estimate for displacement are derived, respectively. Numerical experiments are performed to confirm the theoretical results and the efficiency of the proposed scheme.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2012年第4期425-438,共14页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11061021)
内蒙古自治区高等学校科学研究项目(NJ10006)
内蒙占自然科学基金(2012MS0108)
内蒙古大学研究生培养基金
关键词
电报方程
间断时空有限元方法
最优误差估计
telegraph equation
space-time discontinuous finite element method
optimal order error estimate
